Conic Sections

Conics - Circle General Equation


What is the equation of the circle that passes through the origin, has its center on the line x+y=4,x+y=4, and cuts the circle x2+y26x+16y+24=0x^2+y^2-6x+16y+24=0 orthogonally?

Find the sum of all possible values of b b such that the two points (4,0) (4, 0 ) and (4,0) (- 4, 0) lie on the circle x2+y2+ax+by+c=0 x^2 + y^2 + ax + by +c =0 with radius 6 6 .

If the line y=ax+by=ax+b cuts the circle x2+y24x+8y29=0x^2+y^2-4x+8y-29=0 into two equal parts, then what is the value of 2a+b?2a+b ?

If the circle x2+y2+ax+by+c=0x^2+y^2+ax+by+c=0 passes through three points (1,8),(2,1),(6,1),(-1,-8), (2,1), (6,-1), what is the value of a+b+c?a+b+c ?

If the circle x2+y2+Ax+By+C=0x^2+y^2+Ax+By+C=0 passes through the origin and has the same center as the circle x2+y29x+8y3=0,x^2+y^2-9x+8y-3=0, what is the value of A+B+C?A+B+C?


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